Using the Variational Quantum Thermalizer as an Impurity Solver

The simulation of strongly correlated fermionic systems could potentially benefit from quantum computers which inherently exhibit quantum properties. Calculating a Green's function for an impurity model in the framework of dynamical mean field theory (DMFT) incorporating a quantum device is a particularly efficient way to treat extended materials. We present a novel quantum algorithm to solve such quantum impurity problems, using a hybrid quantum-classical approach. Our solver uses a variational quantum thermalizer to calculate the eigenstates of the system and their energies. Using these states, the Lehmann representation of the impurity Green's function can be measured on quantum devices. By considering the effect of shot noise and quantum errors, which are prevalent on experimental NISQ hardware, we carefully analyze DMFT results for the Bethe lattice and conclude that our algorithm is well suited for current NISQ devices. Finally, we present results from a full DFT+DMFT cycle for real materials systems which show good agreement with reference calculations from classical methods like exact diagonalization and quantum Monte Carlo methods.